From the moment Woody Harrelson swaggers into “LBJ,” you can see the glinting intelligence and hear the thudding heartbeat that he brings to the title character. It couldn’t have been easy. He’s nearly entombed in facial makeup that obscures his own physiognomy — an actor’s landscape — while bringing to life Lyndon B. Johnson, a transitional, still-contentious figure of fascinating contradictions. This was, history tells us, a politician who early in his career spoke against civil rights legislation yet signed the landmark Civil Rights Act of 1964, a president who declared an “unconditional war” on poverty at home even as he escalated the war in Vietnam.

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A preview of the film.Published OnNov. 1, 2017CreditImage by Internet Video Archive

Only some of that history makes it into this disappointing movie, which tracks Johnson’s road from the Senate to the vice presidency and then the presidency, an ascension that culminates with him assuming the role of the nation’s healer after John F. Kennedy’s death. It’s a near-miraculous, compressed coming into consciousness (the movie runs 98 minutes) that develops through different time frames and neatly dovetailing scenes that suggest history is plotted by that great filmmaker in the sky. One moment it’s 1960 and Johnson is weighing his chances as the next Democratic presidential nominee; the next, he is struggling to find a place in the Kennedy administration and vainly looking for political love in the Oval Office.

Mr. Harrelson makes Johnson an almost predictably entertaining force, and his performance fills the movie with oxygen whether he’s barnstorming through politics, slamming down phones, lobbing obscenities, braying at his staff from a toilet seat or gleefully grabbing his crotch while announcing that his tailor needs to make his pants roomier. He’s fun to watch despite the facial makeup, which is so distractingly exaggerated that when I wasn’t thinking of Mrs. Doubtfire I was flashing on the rubbery presidential masks worn by the bank robbers in “Point Break.” It’s a wonder that Mr. Harrelson can convey any emotion through all that latexy blubber much less keep drawing you closer to him. I recognized the similarly encumbered Jennifer Jason Leigh, who plays Lady Bird, only when she started talking.

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Mr. Harrelson as Johnson.CreditSam Emerson/Electric Entertainment

Directed by Rob Reiner from Joey Hartstone’s script, “LBJ” is a frustratingly underdeveloped vehicle for Mr. Harrelson’s talents as well as an unfortunate missed opportunity. Mr. Harrelson hits his beats with charismatic menace and a reverberant Texas twang, but he’s booming in a vacuum. Part of the problem is the filmmakers never figure out why this particular story needed to be told at this specific moment; it feels at once dutiful and arbitrary. That’s too bad, especially given that it could have continued a story told through Obama-era movies — “Selma,” “Jackie,” “Marshall” — that, both directly and obliquely, speak to the present through the convulsions of the 1960s.

Taken together, these movies create a kaleidoscopic portrait of a profoundly changing nation using black, female and marginal characters who once would have remained behind while the white hero went off to write history. They represent, onscreen and off, the very changes that they narrate. With its armies of pale men and next to no black characters, “LBJ” doesn’t look all that different from most other great-man stories. Yet there are moments — Johnson conspiring with a racist power broker played by an excellent Richard Jenkins — when the filmmakers seem ready to shake up the story by laying white, male power bare in all its ugliness. In scenes like these, the movie inches around complexity even as it continues to clear the way for another make-believe savior.